Question

Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for the reaction. (b) How many grams of calcium hydride are needed to form 4.500 g of hydrogen?

Short answer

(a) The balanced chemical equation for the reaction is: CaH_2 + 2 H_2O → Ca(OH)_2 + 2 H_2 (b) 46.955 g of calcium hydride is needed to form 4.500 g of hydrogen gas.

Step-by-step solution

Write the balanced chemical equation for the reaction

The reaction can be represented as follows: CaH_2 + 2 H_2O → Ca(OH)_2 + 2 H_2 This equation is already balanced, as there are an equal number of atoms of each element on both sides.

Convert the given mass of hydrogen gas to moles

To do this, we will use the molar mass of hydrogen gas. Hydrogen has a molar mass of 1.008 g/mol, so H_2 has a molar mass of 2.016 g/mol. Given mass of hydrogen = 4.500 g Molar mass of hydrogen (H_2) = 2.016 g/mol Number of moles = (given mass) / (molar mass) Number of moles of H_2 = 4.500 g / 2.016 g/mol = 2.232 moles

Use stoichiometry to find the moles of calcium hydride

From the balanced chemical equation, we can see that 1 mole of CaH_2 reacts to produce 2 moles of H_2. Now we can set up a proportion to find the moles of CaH_2 needed: 1 (mol CaH_2) / 2 (mol H_2) = x (mol CaH_2) / 2.232 (mol H_2) Solving for x, we find: x = (1 * 2.232) / 2 x = 1.116 moles of CaH_2

Convert moles of calcium hydride to grams

We will now use the molar mass of calcium hydride to convert the number of moles to grams. Calcium has a molar mass of 40.08 g/mol, and hydrogen has a molar mass of 1.008 g/mol, so CaH_2 has a molar mass of 42.096 g/mol. Molar mass of CaH_2 = 42.096 g/mol Moles of CaH_2 = 1.116 moles Mass of CaH_2 = (moles) × (molar mass) Mass of CaH_2 = 1.116 moles × 42.096 g/mol = 46.955 g

Provide the final answer

We found that 46.955 g of calcium hydride is needed to form 4.500 g of hydrogen gas.

Key concepts

Stoichiometry

Stoichiometry is the backbone of chemistry that involves the calculation of reactants and products in chemical reactions. It's like a recipe in cooking - you need the right amounts of ingredients to get the desired dish. In chemical reactions, stoichiometry helps us understand how much of each substance is needed or produced.
When dealing with stoichiometry, we often use the concept of "mole proportion" which allows for the prediction of quantities in a chemical equation. This involves calculating moles, a unit that measures the amount of substance, and using it to determine the relationship between different reactants and products.

Balanced Chemical Equation

A balanced chemical equation is crucial for stoichiometry. It represents how reactants transform into products and ensures the law of conservation of mass is upheld - matter isn't created or destroyed in reactions.
For a balanced reaction, the number of atoms of each element must be the same on both sides of the equation. This balance is important because it reflects real chemical processes.
In the exercise, the chemical equation is:
\[ \text{CaH}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + 2 \text{H}_2 \]
This indicates that one molecule of calcium hydride reacts with two molecules of water to produce one molecule of calcium hydroxide and two molecules of hydrogen gas. It's balanced because each type of atom is conserved throughout the reaction.

Molar Mass

Molar mass is an essential concept in understanding chemical reactions and stoichiometry. It gives the mass of one mole of a substance. Knowing the molar mass helps us convert between the mass of a substance and the number of moles.
For example, in the context of the exercise, knowing the molar mass of hydrogen gas (\( \text{H}_2 \)) is 2.016 g/mol allows us to calculate how many moles are present in a given mass. Similarly, the molar mass of calcium hydride (\( \text{CaH}_2 \)) is 42.096 g/mol, which enables us to determine the mass required for a given number of moles.
This conversion is key to performing accurate stoichiometric calculations.

Calcium Hydride

Calcium hydride, represented as \( \text{CaH}_2 \), is an inorganic compound that reacts with water to release hydrogen gas. It's a useful reactant because it efficiently generates hydrogen, which has various applications, including fuel and research purposes.
In the balanced chemical equation provided, calcium hydride plays the role of a reactant that helps produce both calcium hydroxide and hydrogen gas upon reaction with water. Understanding how calcium hydride interacts in chemical equations helps predict its behavior and calculate its required amounts in reactions.

Hydrogen Gas

Hydrogen gas (\( \text{H}_2 \)) is a diatomic molecule, meaning it consists of two hydrogen atoms. It's a common product in chemical reactions and has significant industrial and scientific importance due to its role in applications such as energy production.
In the exercise, hydrogen gas is formed as a product when calcium hydride reacts with water. To determine how much reactant is needed for a desired amount of hydrogen gas, one must understand stoichiometry and the molar mass of hydrogen.
This fundamental understanding helps in computations where hydrogen is a key component, ensuring correct quantities are used and expected products are achieved.